In order to explain the positive resistance phenomenon of sub-synchronous frequency based on the commonly used fundamental frequency impedance of TCSC, the complex expression of fundamental frequency impedance is derived and selection principle of TCSC conduction angle is proposed. The fundamental frequency reactance of TCSC is capacitive or inductive and its resistance will be negative or positive. The sub-synchronous reactance of TCSC will also be capacitive or inductive and the sub-synchronous resistance is always positive with conduction angle’s influence. Inductive reactance plays a major role for SSR mitigation and power frequency negative resistance provides energy to the positive resistance under sub-synchronous frequency. TCSC conduction angle’s selection should make sure that the reactance should be capacitive under power frequency, and inductive under sub-synchronous frequency, meanwhile the power frequency resistance should be negative. Simulation results show that TCSC can mitigate SSR effectively based on the above basis. It proves rationality of selecting the conduction angle and correctness of the fundamental frequency impedance expression.